Energy released in nuclear fission In induced fission of U-235, neutrons are bombarded at the U-23

ureji1c8r1

ureji1c8r1

Answered question

2022-05-14

Energy released in nuclear fission
In induced fission of U-235, neutrons are bombarded at the U-235, producing U-236. This U-236 then undergoes fission:
U-235 + n --> U-236 --> Ba-141 + Kr-92 + 3n
As far as I understand, the energy released in fission is gained as kinetic energy of the products, and also released as gamma photons/beta particles and neutrinos when the products decay. My confusion lies in calculating the energy released, as I do not think the method in the textbook is correct.
The absorbed neutron loses nuclear potential energy. This causes the binding energy of U-236>U-235, meaning the rest mass of U-236 is less than the rest mass of U-235 + n. This increase in binding energy is then used to deform the nucleus into a double-lobed drop allowing the two fragments to separate due to electrostatic repulsion.
The two fragments formed have a greater binding energy per nucleon than U-236, and hence the binding energy of the fragments is greater than U-236. (In turn causing the mass of the products to decrease). However this increase in binding energy is gained as kinetic energy of the products/released as gamma photons etc.
Mo1 = Mass(U235+n)
Mo2= MassU236
Mo3 = Massfissionproducts
B1=binding energy of U235
B2=binding energy of U236
B3 = binding energy of fission products
The energy released in fission is due to the increase in binding energy B3-B2. The increase in binding energy B2-B1 is used to deform the nucleus - it is not 'released'. Therefore the energy released in the fission process = (Mo2-Mo3)c^2.
However my textbook states that the energy released in the fission process =(Mo1-Mo3)c^2. I don't understand this as they are including the energy to deform the nucleus, (Mo1-Mo2)c^2, when this is not actually released.
Any help is greatly appreciated!

Answer & Explanation

Duncan Cox

Duncan Cox

Beginner2022-05-15Added 18 answers

In principle the energy released is the total energy in (mass of 235 U + energy of thermal neutron) minus the total rest mass of the fission products. In practice, the neutron coming in is thermal (moderated), and has an energy of a few eV, which we can neglect. This means we can compute the energy released from the difference in the rest masses of the "in" and "out" particles. The rest mass of 236 U is not relevant, because what is formed is an excited state.

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